Question

which car is faster, a or b? choose the statement that best fits the graph. a car a is faster than b because a’s speed is 120 m/s. b car b is faster than a because b’s speed is 90 m/s. c car a is faster than b because a’s speed is 20 m/s and b is 15 m/s. d car b is faster than a because b’s motion is accelerating and a is constant speed. graph: distance vs. time, x - axis (distance, m: 0, 30, 60, 90, 120), y - axis (time, sec: 0, 1, 2, 3, 4, 5, 6), two lines (a: red, b: blue) starting at (0,0) and ending at approximate points (100,5) (a) and (90,6) (b)

Explanation:

To determine which car is faster, we calculate the speed (speed = distance/time) for each car from the distance - time graph.

• For Car A: From the graph, when time \(t = 5\) seconds (approximate, looking at the graph's end - point for Car A), the distance \(d = 100\) meters (assuming the y - axis maximum is 100 m). So speed of Car A, \(v_A=\frac{d}{t}=\frac{100}{5}=20\) m/s.
• For Car B: When time \(t = 6\) seconds (approximate, looking at the graph's end - point for Car B), the distance \(d = 90\) meters (since it doesn't reach 100 m at \(t = 6\) s). So speed of Car B, \(v_B=\frac{d}{t}=\frac{90}{6} = 15\) m/s.

Since \(20\) m/s (\(v_A\)) is greater than \(15\) m/s (\(v_B\)), Car A is faster than Car B. Option C states "Car A is faster than B because A’s speed is 20 m/s and B is 15 m/s" which matches our calculation.

Answer:

C. Car A is faster than B because A’s speed is 20 m/s and B is 15 m/s.